Question

Billy Bob and Bob Bob are standing on a plank that is 9.0 m long and has mass 100 kg, that has supports at the 2 m and 5 m marks. Billy Bob has mass 50 kg and is standing on the far left side, while Bob Bob has mass 90 kg and is walking toward the far right side. Will he make it all the way to the end without tipping the plank?

Answer 1

No he will not make it all the way

Step-by-step explanation:

In the attached figure we can see the plank will turn only of the turning moment will be greater than the restoring moment.

balancing moment is created by weight of the plank which acts at the center of the plank thus we have

taking moments about the support A we have

Balancing moment =
`M_(balancing)=100* 2.5* 9.81=2452.5Nm`

The disturbing moment created by bob equals

`M_(disturbing 1)=50* 2* 9.81=981Nm`

The maximum disturbing moment created by bob occurs when he is at the far left side equaling

`M_(disturbing 2)=90* 2* 9.81=1765.8Nm`

Thus the maximum disturbing moment is sum of the above 2 moments

`M_(max)=1765.8+981=2746.8Nm` which is highly greater than the stabling moment thus he will not make it.